The major difference between the Protestant and Jewish Bibles is that the order of the books in each is different. The Protestants arrange the books chronologically, and the Jews arrange them according to the scriptural authority they give the books. (The New Testament is arranged, not chronologically, but according to type: Gospels, history of the early Church, then letters. The Book of Mormon and Doctrine and Covenants are arranged more-or-less chronologically.)
As you can see in Mike Parker’s chart of the Old Testament (which includes a schedule for reading the Old Testament in a year), Jews divide the Old Testament into three parts, each part less authoritative than the last, though all three parts are authoritative: the Law (or “Instruction,” namely the instruction a parent gives to a child), the Prophets, and the Writings. Scriptures such as Acts 28:23 reflect this arrangement. For other scriptures that also reflect it, see Zechariah 7:12; Matthew 5:17, 7:12, and 22:40; Luke 16:16, and 24:44; John 1:45; Acts 13:15 and 24:14; Romans 3:21; 3 Nephi 12:17, 14:12, and 15:10; and D&C 59:22.